EP1402293A1 - Structures de guide d'ondes optiques - Google Patents

Structures de guide d'ondes optiques

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Publication number
EP1402293A1
EP1402293A1 EP02734965A EP02734965A EP1402293A1 EP 1402293 A1 EP1402293 A1 EP 1402293A1 EP 02734965 A EP02734965 A EP 02734965A EP 02734965 A EP02734965 A EP 02734965A EP 1402293 A1 EP1402293 A1 EP 1402293A1
Authority
EP
European Patent Office
Prior art keywords
strip
strips
branch
electrode
waveguide
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
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Application number
EP02734965A
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German (de)
English (en)
Inventor
Pierre Simon Joseph Berini
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Spectalis Corp
Original Assignee
Spectalis Corp
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Publication date
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Publication of EP1402293A1 publication Critical patent/EP1402293A1/fr
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Classifications

    • BPERFORMING OPERATIONS; TRANSPORTING
    • B82NANOTECHNOLOGY
    • B82YSPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y20/00Nanooptics, e.g. quantum optics or photonic crystals
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/10Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
    • G02B6/12Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
    • G02B6/122Basic optical elements, e.g. light-guiding paths
    • G02B6/125Bends, branchings or intersections
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/03Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on ceramics or electro-optical crystals, e.g. exhibiting Pockels effect or Kerr effect
    • G02F1/0305Constructional arrangements
    • G02F1/0316Electrodes
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/21Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference
    • G02F1/225Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference in an optical waveguide structure
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/10Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
    • G02B6/12Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
    • G02B2006/12133Functions
    • G02B2006/1215Splitter
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24Coupling light guides
    • G02B6/26Optical coupling means
    • G02B6/28Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals
    • G02B6/2804Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals forming multipart couplers without wavelength selective elements, e.g. "T" couplers, star couplers
    • G02B6/2821Optical coupling means having data bus means, i.e. plural waveguides interconnected and providing an inherently bidirectional system by mixing and splitting signals forming multipart couplers without wavelength selective elements, e.g. "T" couplers, star couplers using lateral coupling between contiguous fibres to split or combine optical signals
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/09Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on magneto-optical elements, e.g. exhibiting Faraday effect
    • G02F1/095Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  based on magneto-optical elements, e.g. exhibiting Faraday effect in an optical waveguide structure
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/29Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the position or the direction of light beams, i.e. deflection
    • G02F1/31Digital deflection, i.e. optical switching
    • G02F1/313Digital deflection, i.e. optical switching in an optical waveguide structure
    • G02F1/3132Digital deflection, i.e. optical switching in an optical waveguide structure of directional coupler type
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F2203/00Function characteristic
    • G02F2203/06Polarisation independent
    • GPHYSICS
    • G02OPTICS
    • G02FOPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F2203/00Function characteristic
    • G02F2203/10Function characteristic plasmon

Definitions

  • the invention relates to optical devices and is especially applicable to waveguide structures and integrated optics.
  • optical radiation embraces electromagnetic waves having wavelengths in the infrared, visible and ultraviolet ranges.
  • the electromagnetic properties of some metals closely resemble those of an electron gas, or equivalently of a cold plasma.
  • Metals that resemble an almost ideal plasma are commonly termed "noble metals" and include, among others, gold, silver and copper.
  • noble metals include, among others, gold, silver and copper.
  • Numerous experiments as well as classical electron theory both yield an equivalent negative dielectric constant for many metals when excited by an electromagnetic wave at or near optical wavelengths [1 ,2] .
  • the dielectric function of silver has been accurately measured over the. visible optical spectrum and a very close correlation between the measured dielectric function and that obtained via the electron gas model has been demonstrated [3] .
  • TM Transverse Magnetic
  • TM modes In general, only two purely bound TM modes, each having three field components, are guided by an infinitely wide metal film waveguide.
  • the electric field of the modes In the plane perpendicular to the direction of wave propagation, the electric field of the modes is comprised of a single component, normal to the interfaces and having either a symmetric or asymmetric spatial distribution across the waveguide. Consequently, these modes are denoted sb and ab modes, respectively.
  • the sb mode can have a small attenuation constant and is often termed a long-range surface plasmon-polariton.
  • the fields related to the ab mode penetrate further into the metal than in the case of the Sb mode and can be much lossier by comparison. Interest in the modes supported by thin metal films has recently intensified due to their useful application in optical communications devices and components.
  • Metal films are commonly employed in optical polarizing devices [11] while long-range surface plasmon-polaritons can be used for signal transmission [7].
  • leaky modes are also known to be supported by these structures.
  • Infinitely wide metal film structures are of limited practical interest since they offer one-dimensional (1-D) field confinement only, with confinement occurring along the vertical axis perpendicular to the direction of wave propagation, implying that modes will spread out laterally as they propagate from a point source used
  • plasmon-polariton waves guided by a metal-dielectric interface are in general quite lossy. Even long-range surface plasmons guided by a metal film can be lossy by comparison with dielectric waveguides.
  • Known devices exploit this high loss associated with surface plasmons for the construction of plasmon-polariton based modulators and switches.
  • known plasmon-polariton based modulator and switch devices can be classified along two distinct architectures. The first architecture is based on the phenomenon of attenuated total reflection (ATR) and the second architecture is based on mode coupling between a dielectric waveguide and a nearby metal. Both architectures depend on the dissipation of optical power within an interacting metal structure.
  • ATR based modulators make use of this attenuated reflection phenomenon along with means for varying electrically or otherwise at least one of the optical parameters of one of the dielectrics bounding the metal structure in order to shift the angle of incidence where maximum coupling to plasmons occurs. Electrically shifting the angle of maximum coupling results in a modulation of the intensity of the reflected light. Examples of devices that are based on this architecture are disclosed in references [23] to [36]. Reference [42] discusses an application of the ATR phenomenon for realising an optical switch or bistable device.
  • Mode coupling devices are based on the optical coupling of light propagating in a dielectric waveguide to a nearby metal film placed a certain distance away and in parallel with the dielectric waveguide.
  • the coupling coefficient between the optical mode propagating in the waveguide and the plasmon-polariton mode supported by the nearby metal film is adjusted via the materials selected and the geometrical parameters of the device.
  • Means are provided for varying, electrically or otherwise, at least one of the optical parameters of one of the dielectrics bounding the metal. Varying an optical parameter (the index of refraction, say) varies the coupling coefficient between the optical wave propagating in the dielectric waveguide and the lossy plasmon-polariton wave supported by the metal. This results in a modulation in the intensity of the light exiting the dielectric waveguide.
  • References [37] to [40] disclose various device implementations based upon this phenomenon. Reference [41] further discusses the physical phenomenon underlying the operation of these devices.
  • the afore-mentioned co-pending international patent application No. PCT/CAOO/01525 disclosed a waveguide structure comprising a thin strip having finite width and thickness with dimensions such that optical radiation having a wavelength in a predetermined range couples to the strip and propagates along the length of the strip as a plasmon-polariton wave.
  • the strip may comprise a material having a relatively high free charge carrier density, for example a conductor or certain classes of highly-doped semiconductor.
  • the surrounding material may have a relatively low free charge carrier density, i.e. an insulator or an undoped or lightly doped semiconductor.
  • transverse plane i.e.
  • strip sections serve different functions, in some cases in combination with additional electrodes.
  • the strip sections may be discrete and concatenated or otherwise interrelated, or sections of one or more continuous strips.
  • a characteristic of such a thin, finite-width plasmon-polariton waveguide is polarization sensitivity.
  • external radiation linearly polarised along the direction perpendicular to the plane of the strip is coupled effectively to the waveguide in an end-fire arrangement.
  • An object of the present invention is to provide a low-loss polarisation insensitive plasmon-polariton waveguide structure.
  • the present invention seeks to eliminate, or at least mitigate, one or more of the disadvantages of the prior art.
  • a waveguide structure comprising a strip having a substantially square cross-section with dimensions of the same order (less than 10) such that optical radiation having a wavelength in a predetermined range couples to the strip and propagates along the length of the strip as a plasmon-polariton wave.
  • the strip may comprise a material having a relatively high free charge carrier density, for example a conductor or certain classes of highly-doped semiconductor.
  • the surrounding material may have a relatively low free charge carrier density, i.e. an insulator or an undoped or lightly doped semiconductor.
  • Such a strip of finite width offers two-dimensional (2-D) confinement in the transverse plane, i.e. perpendicular to the direction of propagation, and, since suitable low-loss waveguides can be fabricated from such strip, it is useful for signal transmission and routing or to construct components such as couplers, power splitters, interferometers, modulators, switches and other typical components of integrated optics.
  • different sections of the strip serve different functions, in some cases in combination with additional electrodes.
  • the strip sections may be discrete and concatenated or otherwise interrelated, or sections of one or more continuous strips.
  • the optical radiation has a free-space wavelength of 1550 nm
  • the waveguide is made of a strip of a noble metal surrounded by a good dielectric, of about 200 ran to 150 nm, preferably about 180 nm.
  • the strip could be straight, curved, bent, tapered, and so on.
  • the dielectric material may be inhomogeneous, for example a combination of slabs, strips, laminae, and so on.
  • the conductive or semiconductive strip may be inhomogeneous, for example a gold layer sandwiched between thin layers of titanium.
  • the plasmon-polariton wave which propagates along the structure may be excited by an appropriate optical field incident at one of the ends of the waveguide, as in an end- fire configuration, and/or by a different radiation coupling means.
  • the low free-carrier density material may comprise two distinct portions with the strip extending therebetween, at least one of the two distinct portions having at least one variable electromagnetic property, and the device then may further comprise means for varying the value of said electromagnetic property of said one of the portions so as to vary the propagation characteristics of the waveguide structure and the propagation of the plasmon-polariton wave.
  • propagation of the plasmon-polariton wave is supported and, for another value of said electromagnetic property, propagation of the plasmon-polariton wave is at least inhibited.
  • Such embodiments may comprise modulators or switches.
  • Different embodiments of the invention may employ different means of varying the electromagnetic property, such as varying the size of at least one of said portions, especially if it comprises a fluid.
  • the at least one variable electromagnetic property of the material may comprise permittivity, permeability or conductivity.
  • the variable electromagnetic property will be permittivity, which may be varied by applying an electric field to the portion, or changing an electric field applied thereto, using suitable means.
  • the variable electromagnetic property will be permittivity which may be varied by applying a magnetic field to the portion or changing a magnetic field applied thereto, using suitable means.
  • the electromagnetic property may be permittivity and be varied by changing. the temperature of the material.
  • the portion comprises an acousto-optical (photoelastic) material
  • the electromagnetic property may be permittivity and be varied by changing mechanical strain in the material.
  • electromagnetic property will be permeability and may be varied by applying a magnetic field to the material or changing a magnetic field applied thereto, by suitable means.
  • the electromagnetic property will be conductivity or permittivity and may be varied by changing free charge carrier density in said portion, using suitable means.
  • the propagation of the plasmon-polariton wave may be varied by varying an electromagnetic property of the strip.
  • the permittivity of the strip may be varied by changing the free charge carrier density or by changing or applying a magnetic field through the strip.
  • Figures 1(a) and 1(b), labelled PRIOR ART, are a cross-sectional illustration and a plan view, respectively, of a symmetric waveguide structure as disclosed and claimed in copending PCT application No. PCT/CAOO/01525, in which the core is comprised of a lossy metal film of thickness t, width w, length and permittivity & ⁇ embedded in a cladding or background comprising an "infinite" homogeneous dielectric having a permittivity ⁇ i;
  • Figures 2(a) and 2(b) are a cross-sectional illustration and a plan view, respectively, of a symmetric waveguide structure having a substantially square metal cross-section of width w, thickness t, length and permittivity & embedded in a cladding or background comprising an "infinite" homogeneous dielectric having a permittivity ⁇ i;
  • the waveguide cross-section is located in the x - y plane and the metal region is outlined as the rectangular dashed contour.
  • the field distributions are normalized such that max
  • 1;
  • Figures 5(a),(b),(c),(d),(e) and (f) illustrate the spatial distribution of the six field components related to the W mode supported by a square cross-section metal waveguide and the metal region is outlined as the rectangular dashed contour.
  • the field distributions are normalized such that max ⁇ Re ⁇ )
  • 1;
  • Figure 6 shows the spatial distribution of i?e ⁇ E * ⁇ related to the sW mode, plotted in the x direction along the top horizontal edge of the metal region, for waveguides having different cross-sectional dimensions.
  • the spatial distribution of the main transverse electric field component related to the fundamental mode supported by an optical fibre is also shown for comparison;
  • Figure 7 shows the spatial distribution of 7?e ⁇ Ey ⁇ related to the W mode, plotted in the ⁇ ; direction along the top horizontal edge of the metal region, for waveguides having different cross-sectional dimensions.
  • the spatial distribution of the main transverse electric field component related to the fundamental mode supported by an optical fibre is also shown for comparison;
  • Figures 8(a) and 8(b) are a cross-sectional view and a plan view, respectively, of a second embodiment of the invention in the form of an asymmetric waveguide structure formed by a metal region having a substantially square cross-section of thickness t, width w and permittivity ⁇ 2 supported by a homogeneous semi-infinite substrate of permittivity ⁇ i and with a cover or superstrate comprising a homogeneous semi-infinite dielectric of permittivity &;
  • Figures 8(c) and 8(d) give the attenuation of the s$> ⁇ ° and W modes supported by the square cross-section waveguide of Figure 8(a) as a function of dielectric asymmetry;
  • Figure 9 is a plan view of a waveguide with opposite sides stepped to provide different widths
  • Figure 10 is a plan view of a waveguide which is tapered and slanted;
  • Figure 11 is a plan view of a trapezoidal waveguide;
  • Figure 12 is a plan view of a waveguide having curved side edges and suitable for use as a transition piece
  • Figure 13 is a plan view of a curved waveguide section suitable for interconnecting waveguides at a corner;
  • Figure 14 is a plan view of a two-way splitter/combiner formed by a combination of three straight waveguide sections and one tapered waveguide section;
  • Figure 15 is a plan view of an angled junction using a slanted section
  • Figure 16 is a plan view of a power divider formed by a trapezoidal section and pairs of concatenated bends
  • Figure 17 is a plan view of a Mach-Zehnder interferometer formed using a combination of the waveguide sections; waveguide structure of Figure 17;
  • Figures 18(b) and 18(c) are inset diagrams illustrating alternative ways of applying a modulation control voltage
  • Figure 19 is a plan view of a modulator using the Mach-Zehnder waveguide structure of Figure 17 and illustrating magnetic field control
  • Figure 20(a) is a plan view of an edge coupler formed by two parallel strips of straight waveguide with various other waveguides for coupling signals to and from them;
  • Figure 20(b) is an inset diagram illustrating a way of applying a modulation control voltage
  • Figure 21(a) is a perspective view of a coupler in which the parallel strips are not co-planar;
  • Figure 21(b) is an inset diagram illustrating a way of applying a modulation control voltage
  • Figure 22 is a plan view of an intersection formed by four sections of waveguide
  • Figures 23(a) and 23(b) are a schematic front view and corresponding top plan view of an electro-optic modulator employing the waveguide structure of Figure 8(a);
  • Figures 24(a) and 24(b) are a schematic front view and corresponding top view of an alternative electro-optic modulator also using the waveguide structure of Figure 8(a);
  • Figure 24(c) illustrates an alternative connection arrangement of the modulator of
  • Figure 25 is a schematic front view of a third embodiment of electro-optic modulator also using the waveguide structure of Figure 8(a);
  • Figure 26 is a schematic front view of a magneto-optic modulator also using the waveguide structure of Figure 8(a);
  • FIG 27 is a schematic front view of a thermo-optic modulator also using the waveguide structure of Figure 8(a);
  • Figure 28 is a schematic perspective view of an electro-optic switch also using the waveguide structure of Figure 8(a);
  • Figure 29 is a schematic perspective view of a magneto-optic switch also using the waveguide structure of Figure 8(a);
  • FIG 30 is a schematic perspective view of a thermo-optic switch also using the waveguide structure of Figure 8(a);
  • the waveguide structure shown in Figure 2(a) was analysed using the Method of Lines (MoL) applied in a manner similar to that disclosed in the afore-mentioned co- pending PCT/CAOO/01525 application.
  • MoL is a numerical technique that can be used to solve suitably defined boundary value problems based on Maxwell's equations.
  • the method can be used to generate the modes supported by a waveguide structure of interest.
  • the square cross-section waveguide as shown in Figure 2(a) exhibits 90° rotational symmetry about its centre longitudinal axis.
  • a consequence of this property is that many of the modes supported by the structure are degenerate (two or more modes are said to be degenerate with respect to each other if they have identical propagation constants).
  • two of the fundamental modes are degenerate and can be made long-ranging.
  • One of these modes has its main transverse electric field component directed along the x axis and is denoted the sW mode.
  • the other has its main transverse electric field component directed along the y axis and is denoted the W mode.
  • the physical quarter symmetry of the square cross-section waveguide structure is exploited in the MoL when solving for the modes. This is achieved by placing electric and magnetic walls along the y and x axes, respectively, of Figure 2(a), to generate the ssb ⁇ ° mode, and by placing magnetic and electric walls along the y and x axes, respectively, to generate the W mode.
  • is the excitation frequency
  • ⁇ p is the electron plasma frequency
  • the waveguide cross-section is located in the x - y plane and the metal region is outlined as the rectangular dashed contour.
  • the field distributions are normalized such that max I Re
  • 1 and max ⁇ Re ⁇ Ey ⁇
  • 1, respectively.
  • the mode power associated with the ssi ⁇ mode is carried mainly by the Ex and Hy field components.
  • the mode power associated with the W mode is carried mainly by the Ey and Hx field components. It is also observed metal portion, and that they decay in an exponential-like manner away from the metal.
  • Figures 6 and 7 show the spatial distribution of the real part of the Ex and Ey field components associated with the ss» ⁇ ° and W modes, respectively, for the Au core.
  • the distributions are plotted in the x direction along the top horizontal edge of the metal portion and they are shown for various cross-sectional dimensions.
  • the distribution of the main transverse electric field component of the fundamental mode supported by a Single Mode Fibre (SMF) having a numerical aperture of 0.14 and a diameter of 8.2 ⁇ m is also shown on both figures for comparison. All fields are normalised to a maximum value of unity.
  • SMF Single Mode Fibre
  • the overlap factor C in the above is defined as:
  • the fields are normalised such that the following hold: domain over which the waveguide mode fields are computed.
  • the ssb ⁇ ° and W modes are excitable using a simple end-fire technique similar to the one employed to excite surface plasmon- polariton modes [19,6]. This technique is based on maximising the overlap between the incident field and that of the mode to be excited.
  • the present inventor et al. disclosed that plasmon-polariton waves supported by thin metal films of finite width had been observed experimentally at optical communications wavelengths using this method of excitation.
  • direction in the case of the square cross-section waveguides, direction.
  • Introducing such an asymmetry into the structure can break the degeneracy of the W and ssiy 0 modes. If the asymmetry is small, about
  • « 10 " ⁇ then the W and W modes will remain long-ranging as w t is reduced but cut-off dimensions below which purely bound propagation will not occur, are introduced. As the asymmetry
  • Figures 8(c) and 8(d) show the attenuation of the W and W modes as the asymmetry in the structure depicted in Figure 8(a) is increased.
  • the mode can be "cut-off by inducing (electro-optically or otherwise) a modest asymmetry ( ⁇ « 0.5X10 "4 ) to 1.5 ⁇ l0 "4 in the dielectrics surrounding the metal.
  • the long-ranging modes supported by the square cross-section waveguide are quite sensitive to the asymmetry in the structure. This high sensitivity is useful as a small induced asymmetry (created via an electro-optic effect present in the dielectrics say) can effect a large change in the propagation characteristics of the long-ranging modes. This physical phenomenon forms the basis of some of the device architectures described herein.
  • width and thickness of about 40 nm to about 70 nm give good performance.
  • width and thickness of about 500 nm to about 2000 nm give good performance.
  • the waveguide structure 100 shown in Figures 2(a) and 2(b) comprises a strip of finite thickness t and width w of a first material having a high free (or almost free) charge carrier density, surrounded by a second material which has a very low free carrier density.
  • the strip material can be a metal or a highly doped semiconductor and the background material can be a dielectric.
  • Suitable materials for the strip include (but are not limited to) gold, silver, copper, aluminium and highly n- or p-doped GaAs, InP or Si, while suitable materials for the surrounding material include (but are not limited to) glass, quartz, polymer and undoped or very lightly doped GaAs, InP or Si.
  • Particularly suitable combinations of materials include Au for the strip and SiO* for the surrounding material.
  • the thickness t and the width w of the strip are selected equal and small enough such that the waveguide supports two degenerate orthogonally polarised long-ranging plasmon-polariton modes at the free-space operating wavelength of interest.
  • the curves show that very low attenuation values can be obtained with metal strips of practical dimensions.
  • structure dimensions refer to the square cross-section Au waveguides embedded in Si ⁇ 2 at an operating optical free-space wavelength of 1550 nm. Similar dimensions are needed for most material combinations.
  • the plasmon-polariton field may be excited by optical radiation coupled to the strip in an end-fire manner from a fiber butt-coupled to the input of the waveguide.
  • the output of the waveguide can also be butt-coupled to a fibre.
  • the waveguide could be excited at an intermediate position by an alternative means, for example using the so-called attenuated total reflection method (ATR).
  • ATR attenuated total reflection method
  • Figure 9 shows a transition waveguide section 102 having stepped sides which can be used to interconnect two sections of waveguide having different widths.
  • the larger width W2 can be set to about 250 nm to more effectively couple the waveguide to the input/output fibres.
  • the reduced width Wi helps to reduce the insertion loss of the waveguide.
  • a corresponding step in thickness can also be introduced such that each waveguide section has a square cross-section, thus keeping the waveguides polarisation insensitive.
  • Figure 10 shows an angled section 104 which can be used as an interconnect or transition. Its dimensions, Wi, W2 and 1 and the angles ⁇ i and ⁇ 2, are adjusted for a particular application as needed. Usually the angles are kept small, in the range of 1 to 15 degrees and the input and output widths are usually similar. Although the sides of the angled section 104 shown in Figure 10 are tapered, they could be parallel. It should also be appreciated that the angle of the inclination could be reversed, i.e. the device could be symmetrical about the bottom right hand corner shown in Figure 10 or transposed about that axis if not symmetrical about it. The widths Wi and W2 are maintained approximately waveguide.
  • Figure 11 shows a tapered transition waveguide section 106, which can be used to interconnect two waveguides of different widths.
  • the length of the taper is usually adjusted such that the angles are small, usually in the range of 1 to 15 degrees.
  • the taper angles at the two sides are not necessarily the same.
  • Such a configuration might be used as an input port, perhaps as an alternative to the layout shown in Figure 9, or as part of another device, such as a power splitter.
  • Taper profiles other than linear (as shown) could be used, such as exponential, parabolic or sinusoidal.
  • the widths Wi and * are maintained approximately equal to t. Any symmetry of the structure shown can be used.
  • Figure 12 illustrates an alternative transition waveguide section 130 which has curved sides, rather than straight as in the trapezoidal transition section disclosed in Figure 11.
  • the curved sides are shown as sections of circles of radius Ri and R2, subtending angles ⁇ i and ⁇ respectively, but it should be appreciated that various functions can be implemented, such as sinusoidal, exponential or parabolic.
  • the widths Wi and W2 are maintained approximately equal to t.
  • Figure 13 shows a curved substantially square cross-section waveguide section
  • the angle ⁇ of the bend can be in the range of 0 to 360 degrees and the bending radius R can be in the range of a few microns to a few centimetres. For a 45-degree bend, a radius of 0.5 to 2 cm is appropriate.
  • the critical dimensions are the radius R and the positions of the input and output straight sections 100 of substantially square cross-section waveguide.
  • Figure 13 shows no gradual transition between the straight waveguides 100 at the input and output and the ends of the curved section 108, it is envisaged that, in practice, a more gradual offset could be provided so as to reduce edge effects at the corners.
  • Figure 14 shows a two-way power splitter 110 formed from a trapezoidal section
  • the angle between the output waveguides 104 is usually in the range of 0.5 to 10 degrees and their widths are usually similar.
  • the offsets Si and S between the output waveguides and the longitudinal centre line of the trapezoidal section 106 preferably are set to zero, but could be non-zero, if desired, and vary in size. Ideally, however, the output sections 104 should together be equal in width to the wider end 114.
  • Offset Si need not be equal to offset S2 but it is preferable that both are set to zero.
  • the widths of the output sections 104 can be adjusted to vary the ratio of the output powers.
  • the dimensions of the centre tapered section 106 are usually adjusted to minimise input and output reflections and radiation losses in the region between the output sections 104.
  • centre tapered section 106 could have angles that vary according to application and need not be symmetrical.
  • transition section having a width broader than the width of the input waveguide 100 so that the transition section favoured multimode propagation causing constructive/destructive interference patterns throughout its length.
  • the length could be selected so that, at the output end of the rectangular transition section, the constructive portions of the interference pattern would be coupled into the different waveguides establishing, in effect, a 1-to-N power split.
  • Such a splitter then would be termed a multimode interferometer-based power divider.
  • the device shown in Figure 14 could also be used as a combiner.
  • the light would be injected into the waveguide sections 104 and combined by the tapered centre section 106 to form the output wave which would emerge from the straight waveguide section 100.
  • the number of arms or limbs 104 at the output could be far more than the two that are shown in Figure 14.
  • an angled substantially square cross-section waveguide section 104 may be used to form an intersection between two straight substantially square cross-section waveguide sections 100, with the dimensions adjusted for the particular application.
  • the two straight sections 100 are offset laterally away from each other by the distances Oi and O2, respectively, which would be selected to optimise the couplings by reducing radiation and reflection losses, in the manner discussed with reference to Figure 13.
  • the angle of the trapezoidal section 104 will be a factor in determining the best values for the offsets Oi and O2.
  • the sections 100 and 104 need not be connected directly together, but could be spaced by the distances di and d2 and/or coupled by a suitable transition piece that would make the junction more gradual (i.e.
  • Figures 13 and 15 illustrate a general principle of aligning optical fields, conveniently by offsets, wherever there is a transition or change of direction of the optical wave and an inclination relative to the original path, which can cause radiation and reflection if field extrema are misaligned. Such offsets would be applied whether the direction-changing sections were straight or curved.
  • a power divider 116 can also be implemented using a pair of concatenated curved sections 108 instead of each of the angled sections 104 in the nearest to the wider end 114 of the tapered section 106 curves outwards from the longitudinal centre line of the tapered section 106 while the other curved section curves oppositely so that they form an "S" bend.
  • the curved sections in each pair are offset by distance Oi or O2 one relative to the other for the reasons discussed with respect to the bend 108 shown in Figure 13.
  • Figure 17 illustrates a Mach-Zehnder interferometer 118 created by interconnecting two power splitters 110 as disclosed in Figure 14. Of course, either or both of them could be replaced by the power splitter 116 shown in Figure 16.
  • the insertion phase along one or both arms of the device is modified, then destructive interference between the re-combined waves can be induced.
  • This induced destructive interference is the basis of a device that can be used to modulate the intensity of an input optical wave.
  • the lengths of the arms 100 are usually adjusted such that the phase difference in the re-combined waves is 180 degrees for a particular relative change in insertion phase per unit length along the arms. The structure will thus be long if the mechanism used to modify the per unit length insertion phase is weak (or short if the mechanism is strong).
  • Figure 18(a) illustrates a modulator 120 based on the Mach-Zehnder 118 disclosed in Figure 17.
  • parallel plate electrodes 122 and 124 are disposed above and below, respectively, each of the strips 100 which interconnects two angled sections 104, and spaced from it, by the dielectric material, at a distance large enough that optical coupling to the electrodes is negligible.
  • the electrodes are connected in common to one terminal of a voltage source 126, and the intervening strip 100 is connected using a minimally invasive contact to the other terminal. Variation of the voltage V applied by source 126 effects the modulating action.
  • a change in the carrier density of the latter causes a change in its permittivity, which in turn causes a change in the insertion phase of the arm.
  • the change induced in the permittivity is described by the plasma model representing the guiding strip 100 at the operating wavelength of interest. Such model is well known to those of ordinary skill in the art and so will not be described example.) This change is sufficient to induce destructive interference when the waves in both arms re-combine at the output combiner.
  • Figure 18(c) illustrates an alternative connection arrangement in which the two plate electrodes 122 and 124 are connected to respective ones of the teirninals of the voltage source 126.
  • the dielectric material used as the background of the waveguide is electro-optic (LiNbOs, an electro-optic polymer,).
  • the applied voltage V effects a change in the permittivity of the background dielectric, thus changing the insertion phase along the arm. This change is sufficient to induce destructive interference when the waves in both arms re-combine at the output combiner.
  • one voltage source supplies the voltage Vi while the other supplies the voltage V2. Vi and V2 may or may not be equal.
  • the electrodes 122 and 124 could be coplanar with the intervening strip 100, one on each side of it.
  • a high frequency modulator capable of modulation rates in excess of 10 Gbit/s
  • Figure 19 illustrates an alternative implementation of a Mach-Zehnder 128 which has the same set of waveguides as that shown in Figure 17 but which makes use of magnetic fields B applied to either or both of the middle straight section arms to induce a change in the permittivity tensor describing the strips.
  • the change induced in the tensor is described by the plasma model representing the guiding strip at the operating wavelength of interest. Such model is well known to those of ordinary skill in the art and so will not be described further herein.
  • the change induced in the permittivity tensor will induce a change in the insertion phase of either or both arms thus inducing a relative phase difference between the light passing in the arms and generating destructive interference modulates the intensity of the light transmitted through the device.
  • the magnetic field B can be made to originate from current-carrying wires or coils disposed around the arms 100 in such a manner as to create the magnetic field in the desired orientation and intensity in the optical waveguides.
  • the magnetic field may have one or all of the orientations shown, Bx, By or Bz or their opposites.
  • the wires or coils could be fabricated using plated via holes and printed lines or other conductors in known manner.
  • Figure 20(a) illustrates a coupler 139 created by placing two substantially square cross-section waveguide strips 100" parallel to each other and in close proximity over a certain length.
  • the gaps between the input and output of the waveguide sections shown would ideally be set to zero and a lateral offset provided between sections where a change of direction is involved.
  • Curved sections could be used instead of the sections 104, 100 and 100" shown in Figure 20(a). Although only two strips 100" are shown in the coupled section, it should be understood that more than two strips can be coupled together to create an NxN coupler.
  • a voltage can be applied to the two coupled sections 100" via minimally invasive electrical contacts.
  • Figure 20(b) shows a voltage source 126 connected directly to the sections 100" but, if the sections 100, 104 and 100" in each arm are connected together electrically, the source 126 could be connected to one of the other sections in the same arm. Applying a voltage in such a manner charges the arms of the coupler, which, according to the plasma model for the waveguide, changes its permittivity. If, in addition, the dielectric material placed between the two waveguides 100" is electro-optic, then a change in the background permittivity will also be effected as a result of the applied voltage. The first effect is sufficient to change the coupling characteristics of the structure but, if an electro-optic dielectric is also used, as suggested, then both effects will be present, allowing the coupling characteristics to be modified by applying a lower voltage.
  • Figures 21(a) and 21(b) illustrate coupled waveguides similar to those shown in Figure 20(a) but placed on separate layers in a substrate having several layers 140/1, 140/2 and 140/3.
  • the substantially square cross-section waveguide strips could be placed them.
  • the coupled guides can also be offset from each other a distance Sc, as shown in Figures 21(a) and 21(b).
  • Gaps can be introduced longitudinally between the segments of strip if desired and a lateral offset between the straight and angled (or curved) sections could be introduced. Though only two strips are shown in the coupled section, it should be understood that a plurality of strips can be coupled together on a layer and/or over many layers to create an NxN coupler.
  • a voltage source 126 could be connected directly or indirectly to the middle (coupled) sections 100" in a similar manner to that shown in Figure 20(b).
  • an intersection 142 can be created by connecting together respective ends of four of the angled and substantially square cross-section waveguide sections 104, their distal ends providing input and output ports for the device.
  • a prescribed ratio of optical power emerges from the output ports at the opposite side of the intersection.
  • the angles ⁇ i... ⁇ can be set such that optical power input into one of the ports emerges from the port directly opposite, with negligible power transmitted out of the other ports. Any symmetry of the structure shown is appropriate.
  • Various other modifications and substitutions are possible without departing from the scope of the present invention.
  • the waveguide structure shown in Figures 2(a) and 2(b), and implicitly those shown in other Figures have a single homogeneous dielectric surrounding a metal strip, it would be possible to sandwich the metal strip between two slabs of different dielectric material; or at the junction between four slabs of different dielectric material.
  • the multilayer dielectric material(s) illustrated in Figure 21(a) could be used for other devices too.
  • the metal strip could be replaced by some other conductive material or a highly n- or p-doped semiconductor. It is also envisaged that the conductive strip, whether metal or other material, could be multi-layered.
  • Modulation and switching devices will now be described which make use of the fact that an asymmetry induced in optical waveguiding structures having as a guiding element a square cross-section metal strip may inhibit propagation of the main long- ranging degenerate purely bound plasmon-polariton modes supported.
  • the asymmetry in the structure can be in the dielectrics surrounding the metal strip.
  • the permittivity, permeability or the dimensions of the dielectrics surrounding the strip can be different.
  • a dielectric material exhibiting an electro-optic, magneto-optic, thermo-optic, or piezo-optic effect can be used as the surrounding dielectric medium.
  • the modulation and switching devices make use of an external stimulus to induce or enhance the asymmetry in the dielectrics of the structure. As shown in Figures 8(c) and (d), a modest asymmetry- of about 2X10 "4 induced in the dielectrics has a significant deleterious effect on the propagation of the plasmon-polariton wave, thus causing cut-off of the modes.
  • Figures 23(a) and 23(b) depict an electro-optic modulator comprising two metal strips 110 and 112 surrounded by a dielectric 114 exhibiting an electro-optic effect.
  • a dielectric has a permittivity that varies with the strength of an applied electric field. The effect can be first order in the electric field, in which case it is termed the Pockels effect, or second order in the electric field (Kerr effect), or higher order.
  • Figure 23(a) shows the structure in cross-sectional view and Figure 23(b) shows the structure in top view.
  • the lower metal strip 110 and the surrounding dielectric 114 form the optical waveguide.
  • the lower metal strip 110 is dimensioned such that a purely bound long-ranging plasmon- polariton wave is guided by the structure at the optical wavelength of interest.
  • the strip 110 may have a substantially square cross-section, dimensioned such that the two main orthogonally polarised long-ranging plasmon-polariton modes are propagated. Since the guiding lower metal strip 110 comprises a metal, it is also used as an electrode and is connected to a voltage source 116 via a minimally invasive electrical contact 118 as shown.
  • the second metal strip 112 is positioned above the lower metal strip 110 at a distance large enough that optical coupling between the strips is negligible. It is noted that the second strip can also be placed below the waveguiding strip instead of above.
  • the second strip acts as a second electrode.
  • the intensity of the optical signal output from the waveguide can be varied or modulated by varying the intensity of the voltage V applied by the source 116.
  • the waveguiding structure When no voltage is applied, the waveguiding structure is symmetrical and supports plasmon- induced via the electro-optic effect present in the dielectric 114, and the propagation of the plasmon-polariton waves is inhibited.
  • the degree of asymmetry induced may be large enough to completely cut-off the main purely bound long-ranging modes, thus enabling a very high modulation depth to be achieved.
  • a high frequency modulator capable of modulation rates in excess of 10 Gbit/s
  • Figures 24(a) and 24(b) show an alternative design for an electro-optic modulator which is similar to that shown in Figure 23(a) but comprises electrodes 112A and 112B placed above and below, respectively, of the substantially square cross-section metal optical waveguide strip 110 at such a distance that optical coupling between the strips is negligible.
  • Figure 24(a) shows the structure in cross-sectional view
  • Figure 24(b) shows the structure in top view.
  • a first voltage source 116A connected to the metal strip 110 and the upper electrode 112A applies a first voltage Vi between them.
  • a second voltage source 116B connected to metal strip 110 and lower electrode 112B applies a voltage V2 between them.
  • the dielectric material used exhibits a linear electro-optic effect.
  • the waveguide structure shown in Figure 24(c) is similar in construction to that shown in Figure 24(a) but only one voltage source 116C is used.
  • the positive terminal (+) of the voltage source 116C is shown connected to metal strip 110 while its negative terminal (-) is shown connected to both the upper electrode 112A and the lower electrode 112B.
  • first and second portions may be electro-optic according to the desired application and the arrangement of the electrodes and voltage source(s) selected such that a required asymmetry in the permittivity is induced in the structure.
  • Figure 25 shows in cross-sectional view yet another design for an electro-optic modulator.
  • the substantially square cross-section metal waveguide strip 110 is second portion 114E below it.
  • Electrodes 112D and 112E are placed opposite lateral along opposite lateral edges, respectively, of the upper portion 114D of the dielectric 114 as shown and connected to voltage source 116E which applies a voltage between them to induce the desired asymmetry in the structure.
  • the electrodes 112D, 112E could be placed laterally along the bottom portion 114E of the dielectric 114, the distinct portions of the dielectric material still providing the asymmetry being above and below the strip.
  • Figure 26 shows an example of a magneto-optic modulator wherein the substantially square cross-section metal waveguide strip 110 and overlying electrode 112F are used to carry a current / in the opposite directions shown.
  • the dielectric material surrounding the metal waveguide strip 110 exhibits a magneto-optic effect or is a ferrite.
  • the magnetic fields generated by the current I add in the dielectric portion between the electrodes 110 and 112F and essentially cancel in the portions above the top electrode 112F and below the waveguide 110.
  • the applied magnetic field thus induces the desired asymmetry in the waveguiding structure.
  • the electrode 112F is placed far enough from the guiding strip 110 that optical coupling between the strips is negligible.
  • Figure 27 depicts a thermo-optic modulator wherein the substantially square cross- section metal waveguide strip 110 and the overlying electrode 112G are maintained at temperatures 7 and Ti respectively.
  • the dielectric material 114 surrounding the metal waveguide exhibits a thermo-optic effect.
  • the temperature difference creates a thermal gradient in the dielectric portion 114G between the electrode 112G and the strip 110.
  • the variation in the applied temperature thus induces the desired asymmetry in the waveguiding structure.
  • the electrode 112G is placed far enough from the guiding strip 110 that optical coupling between the strips is negligible.
  • modulator devices described above with reference to Figures 23(a) to 27 may also serve as variable optical attenuators with the attenuation being controlled via the external stimulus, i.e. voltage, current, temperature, which varies the electromagnetic property.
  • Figures 28, 39 and 30 depict optical switches that operate on the principle of
  • the input optical signal is first split into N outputs using a power divider; a one-to-two power split being shown in Figures 28, 29 and 30.
  • the undesired outputs are then "switched off' or highly attenuated by inducing a large asymmetry in the corresponding output waveguides.
  • the asymmetry must be large enough to completely cut-off the main purely bound long-ranging mode supported by the waveguide structures of Figures 23, 26 or 27, respectively.
  • the basic waveguide configuration is the same and comprises a substantially square cross-section metal input waveguide section 120 coupled to two parallel substantially square cross-section metal branch sections 122A and 122B by a wedge-shaped splitter 124. All four sections 120, 122A, 122B and 124 are co-planar and embedded in dielectric material 126.
  • the thickness of the metal strips is ds.
  • Two rectangular electrodes 128A and 128B, each of thickness di, are disposed above branch sections 122 A and 122B, respectively, and spaced from them by a thickness d2 of the dielectric material 126 at a distance large enough that optical coupling between the strips is negligible.
  • Each of the electrodes 128A and 128B is wider and shorter than the underlying metal strip 122A or 122B, respectively.
  • the asymmetry is induced electro-optically by means of a first voltage source 130A connected between metal strip 122A and electrode 128A for applying voltage Vi therebetween, and a second voltage source 130B connected between metal strip 122B and electrode 128B, for applying a second voltage V2 therebetween.
  • the asymmetry is induced magneto-optically by a first current source 132A connected between metal strip 122A and electrode 128A, which are connected together by connector 134A to complete the circuit, and a second current source 132B connected between metal strip 122B and electrode 128B, which are connected together by connector 134B to complete that circuit.
  • the asymmetry is induced thermo-optically by maintaining the metal strips 122A and 122B at temperature To and the overlying electrodes 128A and 128B at temperatures Ti and T2, respectively.
  • the dielectric surrounding the metal strip will be electro-optic, magneto-optic, or thermo- optic, or a magnetic material such as a ferrite, as appropriate.
  • any of the sources may be variable.
  • either of the splitter configurations shown in Figures 14 and 16 could be substituted for that shown in Figures 28, 29 and 30.
  • switches shown in Figures 28, 29 and 30 are 1 x 2 switches
  • the invention embraces 1 x N switches which can be created by adding more branch sections and associated electrodes, etc. It will be appreciated that, where the surrounding material is acousto-optic, the external stimulus used to induce or enhance the asymmetry could be determined by the electro-optic material replaced by acousto-optic material and the electrodes 112D and 112E used to apply compression or tension to the upper portion 114D.
  • the various devices embodying the invention have been shown and described as comprising several separate sections of the novel waveguide structure. While it would be feasible to construct devices in this way, in practice, the devices are likely to comprise continuous strips of metal or other high charge carrier density material, i.e. integral strip sections, fabricated on the same substrate.
  • Embodiments of the invention may be useful for signal transmission and routing or to construct components such as couplers, power splitters/combiners, interferometers, modulators, switches, periodic structures and other typical components of integrated optics.
  • HOEKSTRA H. J. W. M., LAMBECK, P. V., KRIJNEN, G. J. M., CTYROKY, J., De MINICIS, M., SIBILIA, C, CONRADI, O., HELFERT, S., PREGLA, R., "A COST 240 Benchmark Test for Beam Propagation Methods Applied to an Electrooptical Modulator Based on Surface Plasmons", Journal of Lightwave Technology, Vol. 16, No. 10, pp. 1921-1926, October 1998.

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Abstract

L'invention concerne un dispositif optique comprenant une structure de guide d'ondes constituée d'une bande (100) composée d'un matériau à densité de porteur de charge libre relativement élevée, entouré d'un matériau à densité de porteur de charge libre relativement faible. La bande possède une largeur (W) et une épaisseur (t) finies, du même ordre que des dimensions telles qu'un rayonnement optique présentant une longueur d'ondes située dans une plage prédéterminée se couple à cette bande, et se propage sur la longueur de cette bande sous forme d'onde plasmon-polariton. De préférence, la largeur et l'épaisseur sont sensiblement égales ou inférieures à environ 300 nanomètres.
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AU2003233704A1 (en) 2002-05-31 2003-12-19 Spectalis Corp. Electro-optic modulators
JP3668779B2 (ja) 2002-07-25 2005-07-06 国立大学法人岐阜大学 光導波装置
US7751112B2 (en) 2008-12-09 2010-07-06 The Invention Science Fund I, Llc Magnetic control of surface states

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